Surface accretion of a pre-stretched half-space: Biot's problem revisited

Motivated by experiments on dendritic actin networks exhibiting surface growth, we address the problem of the stability of this growth process. We choose as a simple, reference geometry a biaxially stressed half-space growing at its boundary. The actin network is modeled as a neo-Hookean material. A kinetic relation between growth velocity and a stress-dependent driving force for growth is utilized. The stability problem is formulated and results are discussed for different loading and boundary conditions, with and without surface tension. Connections are drawn with Biot's 1963 surface instability threshold.